Numerical computation of the genus of an irreducible curve within an algebraic set |
| |
Authors: | Daniel J. Bates Chris Peterson Andrew J. Sommese Charles W. Wampler |
| |
Affiliation: | a Department of Mathematics, Colorado State University, Fort Collins, CO 80525, United Statesb Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, United Statesc General Motors Research and Development, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055, United States |
| |
Abstract: | The common zero locus of a set of multivariate polynomials (with complex coefficients) determines an algebraic set. Any algebraic set can be decomposed into a union of irreducible components. Given a one-dimensional irreducible component, i.e. a curve, it is useful to understand its invariants. The most important invariants of a curve are the degree, the arithmetic genus and the geometric genus (where the geometric genus denotes the genus of a desingularization of the projective closure of the curve). This article presents a numerical algorithm to compute the geometric genus of any one-dimensional irreducible component of an algebraic set. |
| |
Keywords: | 65H10 14Q05 65E05 14H99 |
本文献已被 ScienceDirect 等数据库收录! |
|